Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x+2y &= -2 \\ 3x+5y &= 6\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $5y = -3x+6$ Divide both sides by $5$ to isolate $y$ $y = {-\dfrac{3}{5}x + \dfrac{6}{5}}$ Substitute this expression for $y$ in the first equation. $4x+2({-\dfrac{3}{5}x + \dfrac{6}{5}}) = -2$ $4x - \dfrac{6}{5}x + \dfrac{12}{5} = -2$ Simplify by combining terms, then solve for $x$ $\dfrac{14}{5}x + \dfrac{12}{5} = -2$ $\dfrac{14}{5}x = -\dfrac{22}{5}$ $x = -\dfrac{11}{7}$ Substitute $-\dfrac{11}{7}$ for $x$ back into the top equation. $4( -\dfrac{11}{7})+2y = -2$ $-\dfrac{44}{7}+2y = -2$ $2y = \dfrac{30}{7}$ $y = \dfrac{15}{7}$ The solution is $\enspace x = -\dfrac{11}{7}, \enspace y = \dfrac{15}{7}$.